This invention relates to a composite wheel rim of minimum weight. In this context, minimum weight means the least weight for a wheel rim of a given size, style and strength. Style, in this context implies the design loads and design criteria.
In structural design, minimum weight is achieved when every point in the structure has the same Margin of Safety with respect to stress. When a wheel rim is made of a single ordinary metal, or other quasi-isotropic material, this implies that the stress is the same everywhere. To achieve this condition the rim cross-section is designed to have more material at locations where the load is great and less material where the load is less. In principle the rim cross-section will be reduced or enlarged in accordance with the load at each point.
However, in practice locations requiring little material to carry the load at that point will not be accordingly reduced for other than structural considerations. An element reduced to the minimum needed to carry its load might be too thin (or light or small, etc.) to be handled easily during fabrication. It might be a non-standard gauge or be excessively expensive (or difficult) to make. In such cases excess material finds its way into a design and the wheel rim weight is greater than the minimum required.
The use of composites in the design of structural elements has resulted in a substantial weight savings (in many cases) owing to the low density of the fibers and resins employed. Advanced development attendant on the success of composite designs has brought a ever widening variety of fibers available and with it a range of mechanical properties. Some of the high strength fibers are: graphite, Kevlar (a trademark of DuPont Co.), Boron and several ceramics (i.e. Alumina, Silicon Carbide, Silicon Nitride, Titanium Carbide, etc.). Spectra (a trademark of Allied Signal Inc.) is an example of a low density fiber.
In the early days of composite design, graphite was the fiber of choice for high performance because it was the least dense (of the high performance fibers) as well as having the highest strength to weight ratio. Recently, however, fibers have been developed (i.e., Spectra) that are very strong and much less dense than graphite.
A stylized drawing of the cross-section of a conventional wheel rim is shown in FIG. 1 which includes a pair of rim flanges 10 and a web portion 12. Although thicknesses may vary within the section, material properties are generally uniform (depending on limitations of the manufacturing process). However, the internal load distribution of a wheel rim is due, primarily, to in-plane bending. There are occasions (e.g., banked turns or asymmetrical bumps) when it is also subjected to out-of-plane bending and torsion. Bending stress is proportional to the section modulus (c/I) where:
c--the distance from the neutral axis PA1 I--area moment of inertia about the neutral axis
In-plane bending stress is therefore proportional to c.sub.y /I.sub.x and is maximum for maximum c.sub.y. Similarly, out-of-plane bending stress is proportional to c.sub.x /I.sub.y and is maximum for maximum c.sub.x. A section subjected to bending therefore resists most of the load at its extreme fibers (maximum c.sub.x and c.sub.y). Intervening material resists shear but serves primarily to transfer load between the extremes.
Torsion will be resisted by the section as a whole and by differential bending of all bundles. Differential bending can best be understood by considering the internal loading on an individual fiber bundle. A torsional load imposed on the wheel rim can be decomposed into one or more couples. The shear loads that comprise these couples will load the fiber bundles in transverse shear and they will bend in response. Each fiber bundle will bend differently in accordance with the shears imposed on it. This effect is referred to as differential bending. The aggregate effect of differential bending is a torsional capacity, that is, an ability to resist torsion.
When a section is loaded in bending, the fibers on one side of the neutral axis are put into compression and those on the other side, in tension. The tensile and compression loads are equal, they balance one another.
FIGS. 3A-3F illustrate several different shapes the reinforcing bundles can take. From a structural perspective the preferred form is circular (FIGS. 3B and 3F). It is, structurally, the most efficient. Other considerations (aerodynamics, aesthetics, ease and cost of manufacture, etc.) may impel alternate shapes and some of those are shown in FIGS. 3A, C, E and F.
The primary fiber reinforcing bundles will resist most of the load because of their placement. However, there is an additional effect that results in further optimization. Internal loads tend to distribute in accordance with stiffness. That is, the stiffest load path takes the greatest load. The highest strength fibers are usually also the stiffest. The internal loads will therefore concentrate at the extremes more than they would be if the section had uniform material properties. This will allow the use of less material between the extremes and result in further weight reduction.